CHAPTER 1 INTRODUCTION 1.1 INTRODUCTION TO BUCK CONVERTER In switching power converter control the controller output has one of two states: “ON” or “OFF”. These applications are not well suited to standard linear control design methodologies. A switching technique involving hysteresis is commonly used for these types of power converters. The major drawback of this method is a lack of robustness, so the dead zone is chosen to optimize performance for the nominal plant under one set of conditions. A solution for increasing the system robustness can be the fuzzy control. A fuzzy controller may be intuitively designed with relative simplicity and it has the potential to be very robust. A rough knowledge of the system’s behavior is needed Fuzzy Inference Systems (FIS) can be used to approximate any continuous function and, hence, every continuous control law mapping the state vector into a control action. Unfortunately, fuzzy control has the drawback that proof of stability is generally difficult, and, also, it is sometimes not so intuitive how to improve the performance of a fuzzy controller. For simplicity of design, reliability or economic reasons, the engineer has the problem of deciding on the bang-bang control law for switching power converter. Any way, bang-bang control problems have long been of interest to control engineers, and application of ideas from fuzzy logic in these problems has given recently some useful and interesting results. In the context of the optimal control theory, analyze of the bang-bang control functions has been a special interest because the most controllers have a limited set of output values. It is know that an approximation of an optimal control by a bang-bang function, does not give an optimal bang-bang control.
1
1.2 DC-DC CONVERTERS There are three basic types of dc-dc converter circuits, termed as buck, boost and buck-boost. In all of these circuits, a power device is used as a switch. This device earlier used was a thyristor, which is turned on by a pulse fed at its gate. In all these circuits, the thyristor is connected in series with load to a dc supply, or a positive (forward) voltage is applied between anode and cathode terminals. The thyristor turns off, when the current decreases below the holding current, or a reverse (negative) voltage is applied between anode and cathode terminals. So, a thyristor is to be force-commutated, for which additional circuit is to be used, where another thyristor is often used. Later, GTO’s came into the market, which can also be turned off by a negative current fed at its gate, unlike thyristors, requiring proper control circuit. The turnon and turn-off times of GTOs are lower than those of thyristors. So, the frequency used in GTObased choppers can be increased, thus reducing the size of filters. Earlier, dc-dc converters were called ‘choppers’, where thyristors or GTOs are used. It may be noted here that buck converter (dc-dc) is called as ‘step-down chopper’, whereas boost converter (dc-dc) is a ‘step-up chopper’. In the case of chopper, no buck-boost type was used. With the advent of bipolar junction transistor (BJT), which is termed as self-commutated device, it is used as a switch, instead of thyristor, in dc-dc converters. This device (NPN transistor) is switched on by a positive current through the base and emitter, and then switched off by withdrawing the above signal. The collector is connected to a positive voltage. Now-adays, MOSFETs are used as a switching device in low voltage and high current applications. It may be noted that, as the turn-on and turn-off time of MOSFETs are lower as compared to other switching devices, the frequency used for the dc-dc converters using it (MOSFET) is high, thus, reducing the size of filters as stated earlier. These converters are now being used for applications, one of the most important being Switched Mode Power Supply (SMPS). Similarly, when 2
application requires high voltage, Insulated Gate Bi-polar Transistors (IGBT) are preferred over BJTs, as the turn-on and turn-off times of IGBTs are lower than those of power transistors (BJT), thus the frequency can be increased in the converters using them. So, mostly self-commutated devices of transistor family as described are being increasingly used in dc-dc converters.
Fig [1.1] Buck converter circuit diagram
3
1.3 BUCK CONVERTER Buck converter is a transistor switched by PWM trigger pulses and a diode provides a current continuation path when the transistor is off, thus the input voltage is chopped. A lowpass LC filter is used to attenuate the switching ripple at the output. The input current to a basic buck converter is discontinuous; therefore, in many applications an LC prefilter is applied to reduce EMI. The output voltage vo is related to the input voltage vi by vo = vid and it can be controlled by varying the duty ratio d. Isolated version of a buck converter include forward, push-pull, half-bridge, and bridge converters. Also called chopper or step-down converter.
Fig.[1.2] - Buck converter Block Diagram
4
1.4 THEORY OF OPERATION The name “Buck Converter” presumably evolves from the fact that the input voltage is bucked/chopped or attenuated, in amplitude and a lower amplitude voltage appears at the output. A buck converter, or step-down voltage regulator, provides non-isolated, switch-mode dc-dc conversion with the advantages of simplicity and low cost. Figure [1.2] shows a simplified nonisolated buck converter that accepts a dc input and uses pulse-width modulation (PWM) of switching frequency to control the output of an internal power MOSFET. An external diode, together with external inductor and output capacitor, produces the regulated dc output. Buck, or step down converters produce an average output voltage lower than the input source voltage.
Fig.[1.3] – Switching regulator topology
1.5 EVOLUTION OF A BUCK CONVERTER: The buck converter here onwards is introduced using the evolutionary approach. Let us consider the circuit in Figure [1.4], containing a single pole double-throw switch.
Fig.[1.4] – A resistor with a single-pole double-throw switch 5
For the circuit in Figure [1.4], the output voltage equals the input voltage when the switch is in position A and it is zero when the switch is in position B. By varying the duration for which the switch is in position A and B, it can be seen that the average output voltage can be varied, but the output voltage is not pure dc. The circuit in Figure [1.4] can be modified as shown in Figure [1.5] by adding an inductor in series with the load resistor. An inductor reduces ripple in current passing through it and the output voltage would contain less ripple content since the current through the load resistor is the same as that of the inductor. When the switch is in position A, the current through the inductor increases and the energy stored in the inductor increases. When the switch is in position B, the inductor acts as a source and maintains the current through the load resistor. During this period, the energy stored in the inductor decreases and its current falls. It is important to note that there is continuous conduction through the load for this circuit. If the time constant due to the inductor and load resistor is relatively large compared with the period for which the switch is in position A or B, then the rise and fall of current through inductor is more or less linear, as shown in Figure [1.5].
Fig.[1.5] – Effect of an Inductor
The next step in the evolutionary development of the buck converter is to add a capacitor across the load resistor and this circuit is shown in Figure [1.6]. A capacitor reduces the ripple content in voltage across it, whereas an inductor smoothes the current passing through it. The combined action of LC filter reduces the ripple in output to a very low level. 6
Fig.[1.6] – Circuit with an LC filter
With the circuit in Figure [1.6] it is possible to have a power semiconductor switch to correspond to the switch in position A and a diode in position B. The circuit that results is shown in Figure [1.7]. When the switch is in position B, the current will pass through the diode. The important thing now is the controlling of the power semiconductor switch.
Fig.[1.7] – Buck converter with Load resistor
The circuit in Figure [1.7] can be regarded as the most elementary buck converter without a feedback. The Buck Converter transfers small packets of energy with the help of a power switch, a diode, and an inductor and is accompanied by an output filter capacitor and input filter. This circuit can be further modified by adding the feedback part which is integral for a SMPS because based on the feedback it stabilizes the output. Such a circuit is shown in the Figure [1.8].
7
Fig.[1.8] – Buck converter with PWM controller
The PWM Controller Figure [1.8] compares a portion of the rectified dc output with a voltage reference (Vref ) and varies the PWM duty cycle to maintain a constant dc output voltage. If the output voltage wants to increase, the PWM lowers its duty cycle to reduce the regulated output, keeping it at its proper voltage level. Conversely, if the output voltage tends to go down, the feedback causes the PWM duty cycle to increase and maintain the proper output. A buck converter or step-down switch mode power supply can also be called a switch mode regulator. 1.6 DIFFERENT COMPONENTS IN THE BUCK CONVERTER: As just seen in the previous section that any basic switched power supply consists of five standard components: •
Transistor Switch (Active Switch)
•
Inductor
•
Capacitor
•
Diode (Passive Switch)
•
Pulse-Width Modulating Controller
8
1.6.1 SWITCH In its crudest form a switch can be a toggle switch which switches between supply voltage and ground. But for all practical applications which we shall consider we will deal with transistors. Transistors chosen for use in switching power supplies must have fast switching times and should be able to withstand the voltage spikes produced by the inductor. The input on the gate of the transistor is normally a Pulse Width Modulated (PWM) signal which will determine the ON and OFF time. Sizing of the power switch is determined by the load current and off-state voltage capability. Another new device likely to displace the BJT in many high power applications is the Insulated Gate Bipolar Transistor (IGBT). This device combines the low power drive characteristics of the MOSFET with the low conduction losses and high blocking voltage characteristics of the BJT. Therefore the device is highly suited to high power, high voltage applications.
1.6.1.1 OPERATING FREQUENCY The operating frequency determines the performance of the switch. Switching frequency selection is typically determined by efficiency requirements. There is now a growing trend in research work and new power supply designs in increasing the switching frequencies. The higher is the switching frequency, the smaller the physical size and component value. The reason for this is to reduce even further the overall size of the power supply in line with miniaturization trends in electronic and computer systems.
9
1.6.2 INDUCTOR The function of the inductor is to limit the current slew rate (limit the current inrush) through the power switch when the circuit is ON. The current through the inductor cannot change suddenly. When the current through an inductor tends to fall, the inductor tends to maintain the current by acting as a source. This limits the otherwise high-peak current that would be limited by the switch resistance alone. The key advantage is when the inductor is used to drop voltage, it stores energy. Also the inductor controls the percent of the ripple and determines whether or not the circuit is operating in the continuous mode. 1.6.3 CAPACITOR Capacitor provides the filtering action by providing a path for the harmonic currents away from the load. Output +capacitance (across the load) is required to minimize the voltage overshoot and ripple present at the output of a step-down converter. The capacitor is large enough so that its voltage does not have any noticeable change during the time the switch is off. Large overshoots are caused by insufficient output capacitance, and large voltage ripple is caused by insufficient capacitance as well as a high equivalent-series resistance (ESR) in the output capacitor. The maximum allowed outputvoltage overshoot and ripple are usually specified at the time of design. Thus, to meet the ripple specification for a step-down converter circuit, we must include an output capacitor with ample capacitance and low ESR. The problem of overshoot, in which the output-voltage overshoots its regulated value when a full load is suddenly removed from the output, requires that the output capacitor be large enough to prevent stored inductor energy from launching the output above the specified maximum output voltage.
10
1.6.4 FREEWHEELING DIODE Since the current in the inductor cannot change suddenly, a path must exist for the inductor current when the switch is off (open). This path is provided by freewheeling diode (or catch diode). The purpose of this diode is not to rectify, but to direct current flow in the circuit and to ensure that there is always a path for the current to flow into the inductor. It is also necessary that this diode should be able to turn off relatively fast. Thus the diode enables the converter to convert stored energy in the inductor to the load. 1.6.5 FEEDBACK Feedback and control circuitry can be carefully nested around these circuits to regulate the energy transfer and maintain a constant output within normal operating conditions. Control by pulse-width modulation is necessary for regulating the output. 1.7 CONVENTIONAL PI-PWM CONTROLLER The heart of a switching power supply is its switch control circuit (controller). One of the key objectives in designing a controller for the power converter is to obtain tight output voltage regulation under different line and load conditions. Often, the control circuit is a negative-feedback control loop connected to the switch through a comparator and a Pulse Width Modulator (PWM). The switch control signal (PWM), controls the state (on or off) of the switch. This control circuit regulates the output voltage against changes in the load and the input voltage. PWM is the method of choice to control modern power electronics circuits. Basic idea is to control the duty cycle of a switch such that a load sees a controllable average voltage. To achieve this, the switching frequency (repetition frequency for the PWM signal) is chosen high enough that the 11
load cannot follow the individual switching events and they appear just a “blur” to the load, which reacts only to the average state of the switch. With pulse-width modulation control, the regulation of output voltage is achieved by varying the duty cycle of the switch, keeping the frequency of operation constant. Duty cycle refers to the ratio of the period for which the power semiconductor is kept ON to the cycle period. A clearer understanding can be acquired by the Figure [1.9].
Fig.[1.9] – PWM signal
The Figure [1.9] shows PWM signals for 10% (a), 50% (b), and 90% (c) duty cycles. Usually control by PWM is the preferred method since constant frequency operation leads to optimization of LC filter and the ripple content in output voltage can be controlled within the set limits. The PWM switching at a constant switching frequency is generated by comparing a signal-level control voltage control v with a repetitive waveform as shown in Figure [1.10].
12
Fig.[1.10] – PWM comparator signals
1.8 FUZZY LOGIC - INTRODUCTION Fuzzy logic is a powerful problem-solving methodology with a myriad of applications in embedded control and information processing.fuzzy provides remarkably simple way to draw definite conclusions from vague, ambiguous or imprecise information. In a sense, fuzzy logic resembles human decision making with its ability to work from approximate data and find precise solutions. Unlike classical logic, which requires a deep understanding of a system, exact equations and precise numeric values. Fuzzy logic incorporates an alternative way of thinking, which allows modeling complex systems using a higher level of abstraction originating from our knowledge and experience. Fuzzy logic has been gaining increasing acceptance during the past few years. There are over two thousand commercially available products using fuzzy logic. Fuzzy logic has been found suitable for embedded control applications. Several manufacturers in the automotive industry are using fuzzy technology to improve quality and reduce development time.
13
1.9 DESIGN PROCEDURE 1.9.1 DUTY CYCLE DESIGN This section describes the steps to design the continuos mode buck converter To analyze the voltages of this circuit let us consider the changes in the inductor current over one cycle. From the relation Vx –Vo = L di/dt The change of current satisfies off
di =
∫ (Vx
Vo)dt + / (Vx - Vo)dt
on
For steady state operations the current at the start and the end of a period T will not change. To get a simple relation between voltages we assume no voltage drop across transistor or diode while ON and a perfect switch change. Thus during the ON time Vx=Vin and in the OFF time Vx =0.
Thus
0 = di = /(Vin –Vo)dt + / (-Vo)dt Which simplifies (Vin-Vo)ton – Vo toff = 0 to Vo/Vin = ton/T And defining “duty ratio” as ∂ = ton/T
14
1.9.2 PULSE WIDTH MODULATION OPERATION IN FUZZY Pulse Width Modulation (PWM) technique is a usually technique to control output voltage. The imposed output voltage ripple can be obtained by filtering the output voltage through an appropriate capacitor, C, correlate with variable load, R. An improved dynamic is obtained using a PI controller tuned by different classic or AI techniques (neurofuzzy, genetic algorithms, chaotic etc.).The classical PWM feedback produces in stabilized regime a fixed switching frequency, fsw, which is the frequency of the sawtooth voltage, used to obtain the PWM command for the IGBT switch. The output voltage spectrum is concentrate at the switching frequency and its harmonics and where kp and ωn represent tuning parameters in the frequency. 1.9.3 CONTROLLER DESIGN Conventional control has provided numerous methods for constructing controllers for dynamic systems. Some of these are listed below, • Proportional-integral-derivative (PID) control: Over 90% of the controllers in operation today are PID controllers (or at least some form of PID controller like a P or PI controller). This approach is often viewed as simple, reliable, and easy to understand. Often, like fuzzy controllers, heuristics are used to tune PID controllers (e.g., the Zeigler-Nichols tuning rules). • Classical control: Lead-lag compensation, Bode and Nyquist methods, rootlocus design, and so on. • State-space methods: State feedback, observers, and so on.
15
• Optimal control: Linear quadratic regulator, use of Pontryagin’s minimum principle or dynamic programming, and so on. • Robust control: H2 or H∞ methods, quantitative feedback theory, loop shaping, and so on. • Nonlinear methods: Feedback linearization, Lyapunov redesign, sliding mode control, back stepping, and so on. • Adaptive control: Model reference adaptive control, self-tuning regulators nonlinear adaptive control, and so on. • Stochastic control: Minimum variance control, linear quadratic gaussian (LQG)control, stochastic adaptive control, and so on. • Discrete event systems: Petri nets, supervisory control, infinitesimal perturbation analysis, and so on. Basically, these conventional approaches to control system design offer a variety of ways to utilize information from mathematical models on how to do good control.
16
CHAPTER 2 FUZZY BANG-BANG CONTROL OF BUCK REGULATOR 2.1 THEORY OF CIRCUIT OPERATION A new control technique that implies only a nonlinear controller in the buck feedback is proposed and used. The evaluation of its dynamics and showing the stabilization performances represents the objective The basic idea is to have a small loop gain if the output voltage ripple is small, too, and, if the output voltage ripple increase, the loop gain rise quickly to a value that assure the stability of the overall feedback loop.
Fig [2.1] Block Diagram - Fuzzy Bang-Bang control of Buck Regulator
The supply source is DC voltage source, from which the load is fed through a buck converter comprising a switch, freewheeling diode, LC filter. The switch is controlled by PWM signal, which decides the duty cycle of the converter. In fuzzy logic control the fuzzy controller generates the PWM signal. The fuzzy controller receives to inputs, one is the error signal and the other is the change in error signal. Comparing the output voltage with the desired reference voltage by a comparator generates the error signal. A delay element is 17
used to produce the change in error signal. The delay element may be either a memory of flip-flop. This change in error signal I produced by comparing the present and previous error signals. These two inputs are given to the fuzzy controller. The output from the fuzzy controller produces the PWM signal, which in turn controls the switch’s duty cycle, and the desired output voltage is achieved. 2.2 FUZZY CONTROL The fuzzy controller is composed of the following four elements: 1. A rule-base (a set of If-Then rules), which contains a fuzzy logic quantification of the expert’s linguistic description of how to achieve good control. 2. An inference mechanism (also called an “inference engine” or “fuzzy inference” module), which emulates the expert’s decision making in interpreting and applying knowledge about how best to control the plant. 3. A fuzzification interface, which converts controller inputs into information that the inference mechanism can easily use to activate and apply rules. 4. A defuzzification interface, which converts the conclusions of the inference mechanism into actual inputs for the process.
Fig [2.2] Basic fuzzy controller
18
2.3 FUZZY LOGIC CONTROL FOR BUCK REGULATOR A solution for increasing the system robustness can be the fuzzy control. A fuzzy controller may be intuitively designed with relative simplicity and it has potential to be very robust. A rough knowledge of the system’s behavior is needed. Fuzzy Inference Systems (FIS) can be used to approximate any continuous function and, hence, every continuous control law mapping the state vector into a control action. Unfortunately, fuzzy control has the drawback that proof of stability is generally difficult, and, also, it is sometimes not so intuitive how to improve the performance of fuzzy controller .For simplicity of design, reliability or economic reasons, the engineer has the problem of deciding on the bang-bang control law for switching power converter. Any way, bang-bang control problems have long been of interest to control engineers, and application of ideas from fuzzy logic in these problems has given recently some useful and interesting results. In the context of the optimal control theory, analyze of the bang-bang control functions has been a special interest because the most controllers have a limited set of output values. It is know that an approximation of an optimal control by a bang-bang function does not give an optimal bangbang control. 2.4 FUZZY INFERENCING The process of fuzzy reasoning is incorporated into what is called a Fuzzy Inferencing System. It is comprised of three steps that process the system inputs to the appropriate system outputs. These steps are 1) Fuzzification, 2) Rule Evaluation, and 3) Defuzzification. The system is illustrated in the following figure (2.3).
19
Fig(2.3) Fuzzy inferencing block
2.5 FUZZIFICATION Fuzzification is the first step in the fuzzy inferencing process. This involves a domain transformation where crisp inputs are transformed into fuzzy inputs. Crisp inputs are exact inputs measured by sensors and passed into the control system for processing, such as temperature, pressure, rpm's, etc.. Each crisp input that is to be processed by the FIU has its own group of membership functions or sets to which they are transformed. This group of membership functions exists within a universe of discourse that holds all relevant values that the crisp input can possess. The following figure (2.4) shows the structure of membership functions within a universe of discourse for a crisp input.
20
Fig(2.4)Fuzzification
where: degree of membership: degree to which a crisp value is compatible to a membership function, value from 0 to 1, also known as truth value or fuzzy input. membership function, MF: defines a fuzzy set by mapping crisp values from its domain to the sets associated degree of membership. crisp inputs: distinct or exact inputs to a certain system variable, usually measured parameters external from the control system, e.g. 6 Volts. label: descriptive name used to identify a membership function. scope: or domain, the width of the membership function, the range of concepts, usually numbers, over which a membership function is mapped. Universe of discourse: range of all possible values, or concepts, applicable to a system variable. When designing the number of membership functions for an input variable, labels must initially be determined for the membership functions. The 21
number of labels corresponds to the number of regions that the universe should be divided, such that each label describes a region of behavior. A scope must be assigned to each membership function that numerically identifies the range of input values that correspond to a label. The shape of the membership function should be representative of variable. However this shape is also restricted by the computing resources available. Complicated shapes require more complex descriptive equations or large lookup tables. The next figure shows examples of possible shapes for membership functions.
FIG(2.5) Membership function shapes
When considering the number of membership functions to exist within the universe of discourse, one must consider that: i) Too few membership functions for a given application will cause the response of the system to be too slow and fail to provide sufficient output control in time to recover from a small input change. This may also cause oscillation in the system. ii) Too many membership functions may cause rapid firing of different rule consequents for small changes in input, resulting in large output changes, which may cause instability in the system.
22
These membership functions should also be overlapped. No overlap reduces a system based on Boolean logic. Every input point on the universe of discourse should belong to the scope of at least one but no more than two membership functions. No two-membership functions should have the same point of maximum truth, (1). When two membership functions overlap, the sum of truths or grades for any point within the overlap should be less than or equal to 1. Overlap should not cross the point of maximal truth of either membership function. Marsh has proposed two indices to describe the overlap of membership functions quantitatively. These are overlap ratio and overlap robustness.
Fig(2.6) Slope of membership functions
The fuzzification process maps each crisp input on the universe of discourse, and its intersection with each membership function is transposed onto the μ axis as illustrated in the previous figure. These μ values are the degrees of truth for each crisp input and are associated with each label as fuzzy inputs. These fuzzy inputs are then passed on to the next step, Rule Evaluation.
23
2.6 FUZZY RULES We briefly comment on so-called fuzzy IF-THEN rules introduced by Zadeh. They may be understood as partial imprecise knowledge on some crisp function and have (in the simplest case) the form IF x is Ai THEN y is Bi. They should not be immediately understood as implications; think of a table relating values of a (dependent) variable y to values of an (independent variable) x:
Ai, Bi may be crisp (concrete numbers) or fuzzy (small, medium, Large) It may be understood in two, in general non-equivalent ways: (1) as a listing of n possibilities, called Mamdani's formula:
24
2.7 DEFUZZIFICATION Defuzzification involves the process of transposing the fuzzy outputs to crisp outputs. There are a variety of methods to achieve this, however this discussion is limited to the process used in this thesis design. A method of averaging is utilized here, and is known as the Center of Gravity method or COG, it is a method of calculating centroids of sets. The output membership functions to which the fuzzy outputs are transposed are restricted to being singletons. This is so to limit the degree of calculation intensity in the micro controller. The fuzzy outputs are transposed to their membership functions similarly as in fuzzification. With COG the singleton values of outputs are calculated using a weighted average, illustrated in the next figure. The crisp output is the result and is passed out of the fuzzy inferencing system for processing elsewhere.
Fig(2.7) Crisp output
25
2.8 FUZZY INTERFERENCE SYSTEMS Fuzzy Inference Systems (FIS) can be used to approximate any continuous function and, hence, every continuous control law mapping the state vector into a control action.
2.9 FIS MEMBERSHIP FUNCTIONS
Fig(2.8) FIS Block
FIG (2.9) FIS Input - Error membership function
26
FIG (2.10) FIS Input - Change in error membership function
FIG(2.11) FIS Output membership function
27
2.10 FUZZY ASSOCIATION MEMORY [FAM]
Change in error
Error NB NB NB NM NB NS NB Z NB PS NM PM NS PB Z
NM NB NB NB NM NS Z PS
NS NB NB NM NS Z PS PM
Z NB NM NS Z PS PM PB
PS PM NM NS NS Z Z PS PS PM PM PB PB PB PB PB
PB Z PS PM PB PB PB PB
TABLE [2.1] Fuzzy Rule Table
Based on the relationship between input and output variables a total of 49 rules [corresponding to 49 meaningful states in the FAM table] are composed from the FAM table. Description Negative Big Negative Medium Negative Small Zero Positive Small Positive Medium Positive Big
Fuzzy Association NB NM NS Z PS PM PB
TABLE [2.2] Fuzzy Membership Variables Description
28
2.11 APPLICATIONS OF FUZZY LOGIC SYSTEMS Areas in which fuzzy logic has been successfully applied are often quite concrete. The first major commercial application was in the area of cement kiln control. Other applications, which have benefited through the use of fuzzy systems theory • a navigation system for automatic cars, • predicative fuzzy-logic controller for automatic operation of trains, • laboratory water level controllers, • controllers for robot arc-welders, • feature-definition controllers for robot vision, • graphics controllers for automated police sketchers, and more.
29
CHAPTER 3 MATLAB/SIMULINK MODEL 3.1 CONVENTIONAL BUCK CONVERTER CIRCUIT OPERATION
Fig [3.1] Conventional Buck Converter Circuit
The PWM feedback produces in stabilized regime a fixed switching frequency, which is the frequency of the saw tooth voltage used to obtain the PWM command for IGBT switch .The output volage spectrum is concentrate at the switching frequency and its harmonics and output voltage ripple is higher. 3.2 BUCK REGULATOR OUTPUT The diagram represents the buck regulator output for the circuit under conventional circuit operation. From the DC supply source of 20V the buck converter feeds a load of 20 ohms, 12V. Using the PI controller for producing the PWM signal, the output experiences peak overshoot, that is the output voltage rises above the desired level initially for some time, and then the output
30
gradually reaches a steady state. Correspondingly the PWM duty cycle gets varied. This is shown in the following figure [3.2].
Fig [3.2] Conventional Buck Converter Output
3.3 PWM SIGNAL GENERATION This waveform represents the PWM signal generation of the conventional buck converter circuit in which the saw tooth waveform and the error signal and the corresponding PWM signal is generated. From the following figure [3.3] it can be seen that the error [difference between the actual output voltage and the desired voltage] is initially large, so the pulse width is wider, that is the duty cycle high and as the output voltage builds up, the error get reduced and the pulse width is also getting narrow. After some time duration the output voltage approximately stabilized, but with ripple voltage present in the output. 31
Fig [3.3] PWM Signal Generation
3.4 RESPONSE TO CHANGE IN LOAD When the load current increases from 0.5A to 1.2A the output voltage drops from the desired 12V to undesired 10V for a time period then the output starts to build up to the regulated output of 12V. This voltage dip may cause some of the sensitive loads to malfunction or may not function at all. The behavior of the circuit under change in load current is shown in figure [3.4]. Parameter Peak Overshoot Rise time Settling Time
Value 16 Volts 0.003 Sec. Infinite
Table [3.1] PI-Response to change in Load 32
Fig [3.4] Conventional Buck Converter Under Change In Load
3.5 OPERATION OF BUCK CONVERTER –FUZZY LOGIC CIRCUIT A new control technique that implies the use of fuzzy logic concept to generate the pulse width modulation is employed in which the higher voltage ripple as in the case of conventional circuit is reduced.
Fig [3.5] Fuzzy Logic Employed Buck Converter Circuit 33
3.6 BUCK CONVERTER BLOCK The buck regulator circuit is shown in the figure [3.6] which receives the output generated by the fuzzy PWM block to its switch through port 1 indicated in the figure.
Fig [3.6] Buck Converter Circuit 3.7 FUZZY PWM BLOCK IN THE CIRCUIT The fuzzy controller controlled PWM generation block which is employed in the circuit is shown in the figure [3.7]
Fig [3.7] Fuzzy PWM Block Circuit
34
CHAPTER 4 SIMULATION RESULTS 4.1 FUZZY BANG-BANG CONTROL OF BUCK CONVERTER UNDER CONSTANT LOAD The circuit represents the fuzzy bang-bang control of buck regulator under constant load condition in which the load is kept constant. The circuit is as shown in figure [4.1]
Fig [4.1] Fuzzy Bang Bang Control Of Buck Converter Circuit Under Constant Load
In this circuit shown above figure [4.1] the buck converter is made as subsystem in Matlab. The load connected at the output is 10Ω . With a source DC voltage of 20V constant supply, it is desired to have 12V as Vref at the output. Thus for the constant load connected, the load current will be 1.2Amps. The output voltage is feedback to the PWM circuit where the fuzzy logic controller compares the output with Vref and produces corresponding PWM signal of required duty cycle to the buck converter’s switch. Thus the desired lower output voltage from a high input source is obtained from buck converter. The output waveforms are shown in figure [4.2].
35
4.1.1 OUTPUT UNDER CONSTANT LOAD CONDITION The following waveforms represent the load current and output voltage under constant load conditions. It is shown in figure [4.2].
Fig [4.2] Fuzzy Bang Bang Control Output voltage and current under constant load
It can be seen from the above figure that the output voltage reaches a steady state without any peak overshoot. When the output voltage reaches the desired voltage of 12V, the output gets stabilized. The disadvantages of peak overshoot and ripple voltages are eliminated in the fuzzy bang-bang control. Parameter Peak Overshoot Rise time Settling Time
Value 0 Volts 0.01 Sec. 0.015 Sec
Table [4.1] Fuzzy response under constant Load
4.1.2 PWM GENERATION UNDER CONSTANT LOAD CONDITION 36
The PWM signal generation waveform and the corresponding error signal and the PWM signal is represented figure [4.3].,
Fig [4.3] Fuzzy Bang Bang Control PWM Signal Generation
It can be seen from the above figure that since the load current is constant, the fuzzy controller sends out a constant PWM signal so that the output voltage is maintained constant. The duty cycle remains same during the entire period of the circuit operation.
37
4.2 FUZZY BANG BANG CONTROL OF BUCK CONVERTER UNDER INCREASED LOAD CONDITIONS With the constant load circuit arrangement, an additional 2.5Ω resistor is connected in parallel to increase the load current. The simulation is arranged such that for duration of 0.05 sec the load current is 1.2A with 10Ω resistor alone. After 0.05 sec the breaker is closed so that the 2.5Ω resistor is include in the circuit in parallel with the 10Ω resistor.
Fif [4.4] Fuzzy Bang Bang Control Under Increased Load Condition
With the existing 10Ω load an additional 2.5Ω load is connected in parallel. This reduces the equivalent resistance to 2Ω . So the load current increases from 1.2Amps to 6 Amps. During this heavy increase in load current period the output response of the fuzzy controller is shown in figure [4.5].
38
4.2.1 OUTPUT WAVEFORMS UNDER INCREASED LOAD For the increased load conditions the load current and the output voltage will be as in figure [4.5].
Fig [4.5] Fuzzy Bang Bang Control Under Increased Load Condition Load Current And Output Voltage.
39
4.3 FUZZY BANG BANG CONTROL OF BUCK CONVERTER UNDER CHANGE IN SOURCE VOLTAGE The fuzzy bang bang control of buck converter under change in source voltage is represented in figure [4.6].
Fig [4.6] Fuzzy Bang Bang Control Under Change In Source Voltage.
Here the input source voltage is changed to + 10% of 20V DC, that is from 18V to 22V DC, the source voltage varies. With the help of step input block the input source voltage is kept at 22V DC for 0.08 sec and then the source voltage is reduced to 18V DC. During this period of change in source voltage also the output voltage remains constant at the desired 12V DC at the load terminals. This is shown in figure [4.7].
40
4.3.1 OUTPUT WAVEFORMS WHEN SOURCE VOLTAGE CHANGES For the source voltage change of + 10% of 20V from 22V to 18V DC, the corresponding load current and the output voltage will be as shown in figure [4.7]
Fig [4.7] Load Current , Output Voltage Under Change In Source Voltage
It can be seen from the above figure that during the change in source voltage at 0.08 sec, there is a very minute disturbance at the output which is momentary only and it does not affect the performance of the load.
41
The corresponding PWM signal and fuzzy output signal will be as shown in figure [4.8].
Fig [4.8] PWM Signal And Fuzzy Output Signal
The fuzzy controller sends out the PWM signal until 0.08 sec at the level of 1.15 when the source voltage is 22V DC. When the source voltage reduced at 0.08 sec the fuzzy controller adjusts immediately to the change in source voltage by giving out a high level fuzzy signal of 1.41 to the PWM signal in order to maintain the output voltage at the desired 12V DC by adjusting the duty cycle of the switch in the buck converter.
42
CHAPTER 5 CONCLUSION The proposed control takes the advantages of the bang bang control and of fuzzy control. Its performance are tested and compared with the simulation results obtained with a PI controller. The simulation had shown these advantages.; • High dynamic • Simplicity of design • Reliability • Robustness(FUZZY CONTROL) The fuzzy controller characteristic was designed to minimize the output voltage ripple. The work frequency dependence by buck parameters, input voltage and load level isn’t a problem because in some cases we intentionally modifying the switching frequency in order to reduce the electromagnetic interference.
43
CHAPTER 6 REFERENCES 1.
Nicu Bizon, M. Oproescu, M. Raducu, University of Pitesti, ‘Fuzzy Bang-Bang Control of a Switching Voltage Regulator’ - IEEE international conference on Automation, Quality and Testing, Robotics held on 22-25 May 2008, Vol.2, pages 192-197.
2.
Nicu Bizon, Mihai Oproescu, ‘Energy Generation System Behaviour using a Clocked Fuzzy Peak Current Control’, Proceedings of the 12th European Conference on Power Electronics and Applications, EPE 2007.
3.
K.Viswanathan, D.Srinivasan, R.Oruganti, Department of Electrical and Computer Engineering, National University of Singapore, ‘Universal Fuzzy Controller for A Non-linear Power Electronic Converter’ – IEEE 0783-72808/02 – 2002.
4.
SIMULINK User’s Guide, Math Works Inc., www.mathworks.com
5.
Muhammad
H.Rashid,
‘Power electronics circuits,
devices and
applications’, 2d edition, Prentice-Hall, 1993. 6.
N.Senthil Kumar, K.Sadasivam, K.Prema, ‘Design and Simulation of Fuzzy Controller for Closed Loop Control of chopper fed Embedded DC drives’ – IEEE lntemational Conference on Power System Technology - POWERCON 2004 Singapore, 27-24 November 2004, pages 613-617.
7.
Emil M. Petriu, Dr. Eng., P. Eng., FIEEE Professor, School of Information Technology and Engineering, University of Ottawa, Canada ‘Fuzzy Systems for Control Applications’- http://www.site.uottawa.ca/~petriu/
44